Solved example of express in terms of sine and cosine
Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
Combine $1+\frac{-\sin\left(x\right)}{\cos\left(x\right)}$ in a single fraction
Divide fractions $\frac{\frac{-\sin\left(x\right)+\cos\left(x\right)}{\cos\left(x\right)}}{1+\tan\left(x\right)}$ with Keep, Change, Flip: $\frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}$
Multiply the single term $\cos\left(x\right)$ by each term
Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
Multiplying the fraction by $\cos\left(x\right)$
Simplify the fraction $\frac{\sin\left(x\right)\cos\left(x\right)}{\cos\left(x\right)}$ by $\cos\left(x\right)$
Applying the trigonometric identity: $\tan\left(\theta\right)\cdot\cos\left(\theta\right)=\sin\left(\theta\right)$
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